Explaining Motion:Forces

Chapter Overview (Fall 2002)

A. Newton’s Laws of Motion

B. Free Body Diagrams

C. Analyzing the Forces and Resulting Motion

D. Fundamental Forces

E. Macroscopic Forces

F. Application of Newton’s 2nd Law: One Dimension

G. Application of Newton’s 2nd Law: Two Dimensions

Chapter Overview (Summer 2003)

A. Newton’s Laws of Motion

B. Free Body Diagrams and Application of Newton’s 2nd

Law: Examples

C. Analyzing the Forces and Resulting Motion

D. Fundamental Forces

E. Macroscopic Forces

F. Application of Newton’s 2nd Law: One Dimension

G. Application of Newton’s 2nd Law: Two Dimensions

Illustrating Inertia

• Galileo’s rolling ball’s down and incline

• The hanging mass demonstration

Newton’s 1st Law: Law of Inertia

Every object continues in its state of rest, or of

uniform velocity unless acted upon by an

unbalanced, external force.

The converse should also hold. If a change in the state of

motion is observed, then an unbalanced force is acting on

the object.

Mass and Inertia

Inertia is the tendency of an object to retain its state of motion.

Inertia depends on the amount of matter comprising an object.

Mass is a measure of the amount of matter contained in an

object. Therefore, mass is a measure of inertia. Mass will be

measured in units of kilograms.

Newton’s 2nd Law

The acceleration of an object is directly

proportional to the net force acting on the object,

is in the direction of the net force acting on the

object, and is inversely proportional to the mass

of the object.

The second law may be expressed through the

relationship:

a = F/m

F = m a

Newton’s 2nd Law: Comments

Force, like velocity and acceleration is a vector quantity.

That is you must know its magnitude and direction to

describe it.

The net force is the vector sum of all the forces acting on an

object and is written as F.

The acceleration is always in the direction of the net force.

Forces may originate in a number of different ways (gravity,

electrostatic, tension in a rope etc.). Initially however we

won’t consider the source of the force but instead imagine

springs scales are present to record the strength of the force.

Newton’s 2nd Law: Comments

• The acceleration of an object is proportional to the

net force. There is a linear relationship between

acceleration and net force (graph of acceleration

versus force would be a straight line)

• The acceleration of an object is inversely

proportional to the mass of the object (For a given

force, a larger mass will result in a smaller

acceleration)

Newton’s 2nd Law: Units

[ F] = [m] [a]

[ F] = kg (m/s2)

Newton = kg m/s2

1 Newton is the amount of force needed to

give a 1 kg mass an acceleration of 1 m/s2

Weight

Newton’s 3rd Law

If object A exerts a force on object B, object B exerts

an equal but opposite force on object A.

FAB = - FBA

Newton’s 3rd Law: Comments

Sometimes referred to as the Action-Reaction Law

By Nature, forces exist in pairs

The forces in an action-reaction pair always act on

different objects

Normal Force

Applications of Newton’s 2nd Law 1D Dynamic

Consider a person standing in an elevator

that is accelerating upward. The

upward normal force FN exerted by the

elevator floor on the person is

1. Larger than

2. Identical to

3. Smaller than

The downward weight Fg of the person

Newton’s 2nd Law 1D Dynamic

An 80 kg person is in an elevator that is

accelerating upward at 2 m/s2. Determine

the Normal force acting on the person in the

elevator.

Application of Newton’s 2nd Law

1)Select the object for analysis

2) Draw Free-Body Diagram for the object (later we will include specific expressions relating the strength of various forces to other parameters)

3) Resolve all vector quantities into their x and y components

4) Solve Newton’s 2nd Law for each direction separately

(e.g. Fx = m ax)

Free Body Diagrams

In Free Body Diagrams, arrows are used to

represent each force acting on an object. The

arrows are drawn from the center of mass of

the object and illustrate the vector nature of

the forces acting on an object. The length of

the arrow indicates the strength of the force

and the direction of the arrow shows the

direction of the force.

Free-Body Diagram:Comments

• Anything that is in contact with the object

may exert a force on the object (Gravity

exerts a force without being in contact).

• If the FBD is unbalanced, then the object

will accelerate.

Newton’s 2nd Law 1D Static

Hugh (90 kg) stands on ice partially supported

by a cable around his waste (not neck). The

tension in the cable is 250 N. Determine the

normal force that the ice exerts on Hugh.

What is the normal force exerted by the ice if

the tension increases to 1000 N? What does

this mean?

Newton’s 2nd Law 1D Dynamic

An elevator car with four people (m=1150 kg)

is balanced by a counter weight (m=1000

kg) hanging over a pulley. The motor and

braking system stop working. Determine the

acceleration of the car. Determine the

tension in the cable.

Newton’s 2nd Law 2D Dynamic A sled is being pulled horizontally by two cables as shown

(view looking down). Determine the tension needed in cable A to move the object along the y axis. What is the acceleration of the object?

FTB=6900 N

FTA

6040

Newton’s 2nd Law 2D Static

A 1kg sign is supported by a horizontal rod

and a cable that are attached to a building.

The cable forms a 55 degree angle upward

from the horizontal. Determine the tension

in the cable and the force supplied by the

rod.

Newton’s 3rd Law

The weight of a horse and the normal force

exerted by the ground on the horse

constitute and interaction pair that are

always equal and opposite according to

Newton’s 3rd Law.

Yes

No

Newton’s 2nd Law Dynamic

A 1500 kg car is at rest on an incline (30

degree). What is the maximum acceleration

that the car will experience when the break

is released?

Free-Body Diagram: Examples

• One-dimension no acceleration: Terminal

velocity picture object then FBD

• One-dimension acceleration

• Two-dimension no acceleration: Hanging

sign

• Two-dimension with acceleration

Fundamental Forces of Nature

Gravity

Electromagnetic

Weak Nuclear (Electroweak?)

Strong Nuclear

Newton’s Universal Law of Gravitation

2

21)(r

mmGFFmag gg

Figure

Newton’s Universal Law of Gravitation: Comments

In the figure below an object 1 (of mass m1) exerts an

attractive force F21 on an object 2 (of mass m2). Similarly

object 2 exerts a force F12 on object 1. By Newton’s 3rd

Law these forces are equal in magnitude but opposite in

direction.

Macroscopic Forces

Force Due to Gravity II: Weight

Normal Force

Tension

Friction

Applications 2D

A skier has just begun descending a 30 degree

slope. Assuming that the coefficient of

kinetic friction is .10 calculate her

acceleration and speed after 10 seconds.

The RotorIn an amusement park ride, a small child (m = 30

kg) stands against the wall of a cylindrical room that is then made to rotate. The floor drops downward and the child remains pinned against the wall. The radius of the device is 2.15 m. A frictional force between the child and the wall keeps the child from falling. The coefficient of friction between the child and the wall is 0.400. At what speed must the child rotate to keep from slipping down the wall.

The Rotor

HOMEWORK #7

Chapter 5

Questions 6 and 12

Problems 2, 10, 13, 17, 19, 23, 33

Recommended Problems 5, 8, 16, 18

Compare the maximum speeds

at which a car can safely

negotiate an unbanked turn (r

=50.0 m) in dry weather (µs =

.9) and icy weather (µs = .1)

• A car goes around a tight curve (radius of

50 m) at a speed of 15 m/s. At what angle

must the curve be banked so that the car can

safely negotiate the curve in the absence of

friction?

http://galileo.phys.virginia.edu/classes/109N/

more_stuff/Applets/newt/newtmtn.html

Work and Energy• Work: Effort exerted to accomplish a task

(achieve a goal)

In physics, the effort exerted is the force

(individual or net) applied to an object.

In physics, the achievement is the displacement

of the object.

Only the component of the force in the direction

of the motion does work.

)cos(rFW

Work and Energy: Observations

• Work is a scalar quantity

• Work puts “energy” into or takes “energy”

out of a system (which may be an object)

• Each force acting on an object may do work

the sum of each force’s work is the net work

• Or we may find the net force (some of the

forces) which does net work on the object

• The net work done on a stationary object or

one moving at constant SPEED is zero

Work Energy Modified

A skier (m=70 kg) gliding along a flat surface

with a speed of 12 m/s approaches an 18

incline 12.2 m in length. She stops as she

reaches the top of the incline. Determine the

work done by the frictional force and the

frictional force

Conservation of Mechanical Energy

A ball of mass m =2.60 kg, starting from rest,

falls a vertical distance of .55 cm before

striking a vertical coiled spring which

subsequently compresses by .15 m. What is

the spring constant of the spring?

)(

2

1

2

1

2

1

2

1

2121

2

12

2

11

2

22

2

11

22112211

ffii

ffii

ffii

finalinitial

averageexternalnet

vvvv

vmvmvmvm

vmvmvmvm

pp

tFdtFp

vmp

The combination of Conservation of Momentum and Energy

for a two body elastic collision yields (last class)

)( 2121 ffii vvvv

Conservation of Momentum for a two body elastic collision

ffii vmvmvmvm 22112211

During a rainstorm 0.060 kg/s of water strikes

the roof of a car at a speed of 15 m/s.

Assuming the rain rebounds from the roof at

a speed of 5 m/s, what is the force exerted

by the rain on the roof in 1 s?